James McPherson. Anything that he has written.

I'll echo James McPherson, but I'll also add Bruce Catton, specifically his Army of the Potomac trilogy. You can often find copies of his stuff used, and he reads well and in a narrative vein. Good stuff.

Killer Angels by Michael Shaara won a Pulitzer Prize for nonfiction. It's about Gettysburg and General Lee is one of the 'characters.'

Ed Ayers's In the Presence of Mine Enemies; he looks at two counties in the Shenandoah Valley, one northern and one southern, in the leadup to and during the war. He gathered all the primary sources on both of them, and used it to hold himself to strict scholarly discipline in writing about the Civil War. The way he phrased it, it's too easy to just find 200 quotes that support any position on the war when you can pick from any time or place in the country. He looks at how the lives of ordinary people in these counties shaped and were shaped by the history of the war, emphasizing the contingency and uncertainty in a war that often becomes stale with retelling.

Also recommend Ethan Rafuse, doing good work shaking up the often derivative consensus on the war. I personally think he gets a little to attached to certain pet ideas, but he produces great operational narratives.

Gary Gallagher is a favorite too; he focuses a lot on Confederates, and Lee in particular, because he really is one of the towering figures of the war. See Lee and His Army in Confederate History and Lee the Soldier. Very much has put his foot down on the question of if the Confederacy was a real nation; it walked like a duck and quacked like a duck.

Mark Grimsley wrote a great book about Union civil-military policy called The Hard Hand of War.

Joseph E. Glatthaar has published General Lee's Army: From Victory to Collapse and Soldiering in the Army of Northern Virginia: A Statistical Portrait of the Troops who Served Under General Lee, and Forged in Battle, which covers the history of U.S. Colored Troops.